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A Model for Cavity Induced Errors with Wavefront Slope in High Accuracy Spherical Fizeau Metrology (ABSTRACT)

A paper by Sykora of Zygo showing that the Random Ball Test (RBT) works less and less precisely as the numerical aperture of the transmission sphere becomes smaller. In other words, the RBT works best for fast transmission spheres and another means of calibration should be used for slow test optics.

A Practical Implementation of the Random Ball Test (ABSTRACT)

ABSTRACT: The random ball test for calibrating interferometer transmission spheres was reported about 8 years ago but there did not appear to be an ideal ball. Now, nearly ideal balls are available. The paper describes commercially available hardware for performing the random ball test and example results from the test.

A Simple Ball Averager for Reference Sphere Calibrations (ABSTRACT)

ABSTRACT: A paper by authors at NIST about simulations and experiments done with the Random Ball Test (RBT) giving criteria for establishing the precision of transmission sphere calibration using the RBT.

Absolute Measurement of Surface Roughness (ABSTRACT)

ABSTRACT: A paper by Creath and Wyant explaining the method of calibration of surface roughness interferometers. This same method is used in the Random Ball Test (RBT) except that the random surface over which interferograms are averaged is not a plane but a sphere.

Aligning a Parabola to an Autocollimating Flat Mirror (ABSTRACT)

ABSTRACT: An autostigmatic microscope is a perfect way of aligning an autocollimating flat mirror to a parabola. This notes descibes the simple two step process of positioning the PSM objective focus coincident with the focus of the parabola.

Aligning Optical Elements to a Common Axis (ABSTRACT)

ABSTRACT: It is sometimes necessary to align a series of optical elements, lenses and mirrors, to a single, straight optical axis. This note describes a method using an autostigmatic microscope (ASM) where the ASM is moved along a straight line relative to the axis of the bench in which the elelemts are mounted so the centers of curvature of the elements can be adjusted to lie on the line or axis of the system.

Alignment of 4-Mirror Wide Field Corrector for the Hobby-Eberly Telescope (ABSTRACT)

ABSTRACT: Paper by Oh describing the use of an autostigmatic microscope (PSM) to precisely position computer generated hologram (CGH) alignment targets on optical surfaces.

Alignment of Optical Systems (ABSTRACT)

ABSTRACT: Describes the advantages of aligning optical systems using a Point Source Microscope (PSM) where the optical axis of the system is folded in 2 or 3 dimensions  and shows how pseudo aberrations can be generated that show quantitatively the degree of precision of the alignment from the Star image seen in the PSM.

Calculating BTDF from Window Surface Roughness (ABSTRACT)

ABSTRACT: Stover, et. al., show that scatter in transmission through a window may be calculated from surface roughness in a manner similar to calculating BRDF from roughness for a reflecting surface.

Calculation of the Vertex Radius of an Off Axis Parabolic Surface using the Sag Measured with a Three Ball Spherometer (ABSTRACT)

ABSTRACT: A paper by An and Parks describing a method of calculating the vertex radius of an off-axis parabolic segment using a three ball spherometer to measure the sag. The vertex radius is found by solving a set of six simultaneous, non-linear equations for the three coordinates of the ball centers and the corresponding three coordinates of the point of contact of the ball with the parabolic surface.

Calibration of Interferometer Transmission Spheres (ABSTRACT)

ABSTRACT: A readable copy of the original paper on the Random Ball Test (RBT) authored at NIST that was published in a non-archival meeting journal. Even here the figures are not legible. For better example figures see "A practical implementation of the random ball test".

Calibration of Spherical Reference Surfaces for Fizeau Interferometry (ABSTRACT)

ABSTRACT: A study by Burke and Wu of CSIRO comparing several methods of transmission sphere calibration that concludes the Random Ball Test (RBT) has the highest precision of all the methods tried though it is tedious to perform for highest precision if the RBT is not automated.

Centering Steep Aspheric Surfaces (ABSTRACT)

ABSTRACT: We describe a method of finding the optical axis of an aspheric surface by looking at an annulus of the surface as the surface is rotated in azimuth. The method uses either an autostigmatic microscope or an interferometer to view the annulus. Distinctive features of the reflected spot movement, or the changes in Zernike coefficients found with interferometry while the surface is rotated in azimuth permits the separation of decenter from tilt. The method appears to be suitable for use with any aspheric surface.

Centering with the PSM (ABSTRACT)

ABSTRACT: Desribes step-by-step how to calculate the locations of the centers of curvature of optical elements to be centered, and how to set up one or two PSM's to center the lenses as they are assembled on a rotary table. Also discussed are practical issues relating to the hardware, and calculation of sensitivites to alignment.

Computer Generated Holograms as Fixtures for Testing Optical Elements (ABSTRACT)

ABSTRACT: Custom patterns on computer generated holograms (CGH) are designed as centers of balls when interrogated with an autostigmatic microscope. Physical balls matched to these centers to micrometer tolerances serve as datums for optical elements.

Case Studies & Testimonials

  • "You are always responsive and give us lots of useful information!!"

    Dr. Shaojie Chen
    Dunlap Institute for Astronomy and Astrophysics
    University of Toronto


  • "As always we are very much loving the instrument, I personally love the camera upgrade from what I'm used to!"

    Weslin Pullen
    Hart Scientific Consulting International, LLC
    Tucson, Arizona


  • The PSM is an ideal tool for finding the center of curvature of a ball or the axis of a cylinder. The question is for how small a ball or cylinder can the PSM do this?

    The smallest article that was readily available was a piece of monofilament 8 pound test fishing line that was 290 μm in diameter. There was no problem finding the axis of the fishline, and separating the Cat’s eye reflection from the surface from the confocal reflection of the axis. The experiment was done with a 5x objective, and the result would have been even more definitive using a 10x objective.

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清 原 耕 輔   Kosuke Kiyohara
清原光学 営業部   Kiyohara Optics / Sales
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